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统计学 概率Consider 3 boxes.The first box contains 1 white and 2

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统计学 概率
Consider 3 boxes.The first box contains 1 white and 2 black balls,the second box contains 2 white and 4 black,and the
third box contains 6 white and 3 black.Toss a fair die and randomly choose a ball
- from the first box if you roll a 1.
- from the second box if you roll an even number.
- from the third box if you roll a 3 or a 5.
a) Find the probability that the chosen ball is white.
b) Given that the chosen ball is black,find the probability that it was drawn from the second box.
c) Consider five repetitions of the experiment (rolling the dice then drawing a ball),replacing the ball after each trial.What
is the probability that you select twice from box 1,twice from box 2 and once from box
a)1/6*1/3+3/6*2/6+2/6*6/9=4/9
b)由P(A/B)=P(AB)/P(B)得,
p=(3/6*4/6)/(1-4/9)=3/5
c)10*(1/6)^2 * 3*(3/6 )^2 * 2/6=5/6
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